\section{Review of the Weyl Tensor}

Recall the Weyl Tensor is given by
\begin{equation}
C_{\rho\sigma\mu\nu} = R_{\rho\sigma\mu\nu} -
\frac{1}{2}(g_{\rho\[\mu}R_{\nu]\sigma} - g_{\sigma[\mu}R_{\nu]\rho}) +\frac{R}{3}g_{\rho[\mu}g_{\nu]\sigma}.
\end{equation}
